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\usepackage[croatian, english]{babel}
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\def\tr{{\mbox{$\triangle$}}}
\def\du{{\mbox{\rm d$u$}}}
\def\dx{{\mbox{\rm d$x$}}}
\def\df{{\mbox{\rm d$f$}}}
\def\dr{{\mbox{\rm d$r$}}}
\def\dt{{\mbox{\rm d$t$}}}
\def\dy{{\mbox{\rm d$y$}}}
\def\dz{{\mbox{\rm d$z$}}}
\def\dfi{{\mbox{\rm d$\varphi$}}}
\def\dro{{\mbox{\rm d$\rho$}}}
\def\ds{{\mbox{\rm d$s$}}}
\def\tg{{\mbox{\rm tg\,}}}
\def\arctg{{\mbox{\rm arc\,tg\,}}}
\def\arcsin{{\mbox{\rm arc\,sin\,}}}
\def\arccos{{\mbox{\rm arc\,cos\,}}}
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%%%%%%%%%%%% ODAVDJE POČINJE DOKUMENT


\begin{document}






\renewcommand{\thesection}{}

\section{Prvi parcijalni iz Analize III, 18.04.2013.}
\setcounter{zad}{0}



\vspace*{5mm}
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onlyText=true,%
floatPos=htb,%
capWidth=1.0,% of \columnwidth
capPos=r,%
capVPos=c,%
objectPos=l]%
{}%
{\includegraphics{iks_na_kvadrat}}%
[e]{{
\begin{zad}
Funkciju definisanu grafikom razviti u Furijer-ov red. Dobijeni rezultat iskoristiti za sumiranje redova\\
\hspace*{5mm}
($a$) $\displaystyle{1-\frac{1}{2^2}+\frac{1}{3^2}-\frac{1}{4^2}+...}$;\\
\hspace*{5mm}
($b$) $\displaystyle{1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...}$.
\end{zad}}}
{fig:text}

\begin{zad}
Ako je $f(x)=\displaystyle{\arcsin\frac{x}{y}}$ gdje je $y=\sqrt{x^2+1}$ provjeriti da li je $\displaystyle{\frac{\df}{\dx}=\frac{1}{x^2+1}}$.
\end{zad}

\begin{zad}
Odrediti ekstreme funkcije $f(x,y)=xe^{y+x\sin y}$.
\end{zad}

\begin{zad}
Izračunati:

(a) dvostruki integral $\displaystyle{\int_0^{2\pi}\dfi\int_{0}^a\rho^2\sin^2\varphi\,\dro}$;

(b) dvojni integral $\displaystyle{\iint\limits_G\frac{xy\sqrt{1-x^2-y^2}}{2x^2+y^2}}\dx\dy$ gdje je $G=\{(x,y):x^2+y^2\le 1, x\ge0, y\ge0 \}.$\\


Napomena: dio pod ($a$) "nosi" 30\% zadatka dok dio pod ($b$) 70\%.
\end{zad}




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\vspace*{5mm}


\renewcommand{\thesection}{}

\section{Prvi parcijalni iz Analize III, 18.04.2013.}
\setcounter{zad}{0}



\vspace*{5mm}
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onlyText=true,%
floatPos=htb,%
capWidth=1.0,% of \columnwidth
capPos=r,%
capVPos=c,%
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{}%
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[e]{{
\begin{zad}
Funkciju definisanu grafikom razviti u Furijer-ov red. Dobijeni rezultat iskoristiti za sumiranje redova\\
\hspace*{5mm}
($a$) $\displaystyle{1-\frac{1}{2^2}+\frac{1}{3^2}-\frac{1}{4^2}+...}$;\\
\hspace*{5mm}
($b$) $\displaystyle{1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...}$.
\end{zad}}}
{fig:text}

\begin{zad}
Ako je $f(x)=\displaystyle{\arcsin\frac{x}{y}}$ gdje je $y=\sqrt{x^2+1}$ provjeriti da li je $\displaystyle{\frac{\df}{\dx}=\frac{1}{x^2+1}}$.
\end{zad}

\begin{zad}
Odrediti ekstreme funkcije $f(x,y)=xe^{y+x\sin y}$.
\end{zad}

\begin{zad}
Izračunati:

(a) dvostruki integral $\displaystyle{\int_0^{2\pi}\dfi\int_{0}^a\rho^2\sin^2\varphi\,\dro}$;

(b) dvojni integral $\displaystyle{\iint\limits_G\frac{xy\sqrt{1-x^2-y^2}}{2x^2+y^2}}\dx\dy$ gdje je $G=\{(x,y):x^2+y^2\le 1, x\ge0, y\ge0 \}.$


Napomena: dio pod ($a$) "nosi" 30\% zadatka dok dio pod ($b$) 70\%.
\end{zad}




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\end{document}
